Exponential Decay Calculator

Step-by-Step Guide to Using the Exponential Decay Calculator

Introduction

The Exponential Decay Calculator is a tool designed to help you understand how quantities decrease over time through a decay process. This guide will walk you through each step to efficiently use this calculator and obtain the results you need.

Step 1: Input the Initial Amount

To begin, locate the input field labeled Initial Amount (A₀). Enter the starting amount of the substance or quantity you are considering. Make sure the value is greater than 0.0001 as this is a required field and needs to be validated.

Step 2: Enter the Decay Constant

Next, move to the field labeled Decay Constant (λ). This field represents the rate at which the quantity decays. Enter a positive number within the range of 0.0001 to 1000. This field is crucial as it determines the speed of the decay process. Ensure it’s required and validated.

Step 3: Input the Time

Proceed to the Time (t) field and enter the duration for which the decay process will occur. This is also a required field and must be zero or a higher value. The time value will affect how much of the initial quantity remains after decay.

Step 4: Select the Time Unit

The next step involves selecting the Time Unit. You will find a dropdown menu with options like Seconds, Minutes, Hours, Days, and Years. This field is critical because it defines the unit of time that will be used in calculations and there must be an option selected.

Step 5: Obtain the Results

• Remaining Amount (A): The calculator will use the formula initialAmount * exp(-decayConstant * time) to determine the remaining quantity after decay. The result will be displayed with four decimal places.
• Amount Decayed: This calculation uses the logic initialAmount - remainingAmount to show how much of the initial quantity has decayed, formatted to four decimal places.
• Percentage Remaining: Calculated as (remainingAmount / initialAmount) * 100, this result shows the percentage of the initial amount that remains, formatted to two decimal places as a percentage.
• Half-Life: The half-life is calculated using the formula ln(2) / decayConstant. This value represents the time required for half of the initial quantity to decay, displayed with two decimals and the same time unit used for the calculation.

Conclusion

Following these steps will enable you to effectively utilize the Exponential Decay Calculator, providing you with critical insights about the decay process of the quantity you’re analyzing. Ensure all required fields are correctly filled and validated before reviewing the results.